A Note on the Definition of Bounded Variation of Higher Order for Double Sequences
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Authors: B. L. GHODADRA AND V. FüLöP
DOI: 10.46793/KgJMat2004.563G
Abstract:
In this study the definition of bounded variation of order p (p ∈ ℕ) for double sequences is considered. Some inclusion relations are proved and counter examples are provided for ensuring proper inclusions.
Keywords:
Double sequence of bounded variation, double sequence of bounded variation of order p (p ∈ ℕ), double sequence of bounded variation of order (p, 0), double sequence of bounded variation of order (0,p), double sequence of bounded variation of order (p,p).
References:
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[2] J. W. Garrett, C. S. Rees and Č. V. Stanojević, L1-convergence of Fourier series with coefficients of bounded variation, Proc. Amer. Math. Soc. 80(3) (1980), 423–430.
[3] K. Kaur, S. S. Bhatia and B. Ram, Double trigonometric series with coefficients of bounded variation of higher order, Tamkang J. Math. 35(3) (2004), 267–280.
[4] F. Móricz, Convergence and integrability of double trigonometric series with coefficients of bounded variation, Proc. Amer. Math. Soc. 102(3) (1988), 633–640.
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